Title: Direct and inverse elastic scattering by unbounded rough surfaces

报告人：张海文 中国科学院数学与系统科学研究院

Abstract: This talk is concerned with the direct and inverse scattering problems of time-harmonic elastic waves by an unbounded rigid rough surface. A Nyström method is proposed for the direct scattering problem based on the integral equation method. Convergence of the Nyström method is established with convergence rate depending on the smoothness of the rough surfaces. In doing so, a crucial role is played by analyzing the singularities of the kernels of the relevant boundary integral operators. Numerical experiments are presented to demonstrate the effectiveness of the method. Moreover, a direct imaging method is developed to reconstruct the unbounded rough surface from the elastic scattered-field data. A Helmholtz-Kirchhoff-type identity is derived and then used to provide a theoretical analysis of the direct imaging algorithm. Numerical experiments are presented to show that the direct imaging algorithm is fast, accurate and robust with respect to noise in the data.

报告人简介：张海文，中国科学院数学与系统科学研究院副研究员。2013年博士毕业于中国科学院数学与系统科学研究院。研究方向为声波、弹性波与电磁波反散射问题。2018年获全国反问题年会青年学术奖。2019年入选中国科学院数学与系统科学研究院“陈景润未来之星”计划。2021年入选中国科学院“青年创新促进会”会员。在 SIAM J. Appl. Math.、SIAM J. Imaging Sci.、SIAM J. Sci. Comput.、Inverse Problems、J. Comput. Phys. 等学术期刊上发表论文20余篇。

时间：2021年11月20日（周六）10:00-11:00

地点：腾讯会议ID: 364 071 937

邀请人：孟宪昌  数学学院教授